The change is being valued at rates that don't fit

This is the second half of every variation argument, and often the more expensive half. The change is admitted, then the other side's quantity surveyor prices it at contract rates tendered for different conditions, or a pro-rata that ignores the disruption, while your dayworks records, the hour-by-hour cost of doing it, go unread. The number lands and you are told that is the mechanism.

But valuation is not a discretion, it is a hierarchy. The contract says when contract rates apply, when they must be adjusted, when new rates built for the changed work, called star rates, or a fair valuation take over, and when dayworks are the right measure. Which rung applies is an argument about the character and conditions of the work, fought with your own records: what changed, what it disturbed, what it actually cost.